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Moisture transport properties of polyamides copolymers intended for food packaging applications
Journal of Food Engineering 53 (2002) 287–293 www.elsevier.com/locate/jfoodeng
Moisture transport properties of polyamides copolymers intended for food packaging applications M.A. Del Nobile b
a,*
, G.G. Buonocore
a,b
, L. Palmieri a, A. Aldi a, D. Acierno
a,b
a Instituto di Produzioni e Preparazioni Alimentari, University of Foggia, Via Napoli, 25 71100 Foggia, Italy Department of Materials and Production Engineering, University of Naples ‘Federico II’, P.le Tecchio 80, 80125 Naples, Italy
Received 16 March 2001; accepted 11 September 2001
Abstract In this paper the barrier properties of a series of polyamides used for food packaging applications were analyzed. In particular, permeation of water through the investigated polyamides was studied and water diffusivity and solubility were evaluated as a function of water concentration. Water vapor sorption tests were performed at 25 °C and at several water vapor activities on the four samples investigated. The obtained values were related to the macromolecular chain modification deriving from the introduction of different comonomers. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Water; Nylon; Sorption; Diffusion; Packaging
1. Introduction Polymeric materials are generally used in food packaging applications because they have, among other features, the capability to control the mass exchange of low molecular weight compounds between the foodstuff and its external environment. It is extremely important to guarantee the proper shelf life of the packed product. In fact, it must be considered that the degradation rate of the packed foodstuff can be decreased if the packaging material presents high barrier properties toward those specific compounds responsible for food degradation. Transport properties of oxygen, carbon dioxide, water, nitrogen and aromas through polymers are usually the more interesting to be assessed. The permeability of low molecular weight compounds through polymers usually spans a wide range of values permitting proper choice of the packaging materials for specific needs. Actually, the desired characteristics of a packaging material are obtained by laminating films with different properties. New materials based on polyamides can be developed, which present intrinsic barrier properties. In this way, the thickness of the film can be reduced and this can be considered an environmental advantage. *
Corresponding author. E-mail address: [email protected] (M.A. Del Nobile).
In the present paper water transport properties have been evaluated for polyamides, polymers generally used in packaging applications. In particular, the effect of copolymerization of Nylon 6,6 on its barrier properties has been studied. Different comonomers have been used and the different packaging materials obtained were characterized to understand how chemical and physical modifications of the polymer structure influence water permeability with respect to the homopolymer [an homopolymer is defined as a polymer consisting of chains that contain a single repeating unit (Rosen, 1982)].
2. Experimental 2.1. Materials The polyamide samples were supplied by SNIA Ricerche (Via Pomarico s.n.c. 75010 Pisticci Scalo Italy) as films, and were used as received. 2.2. Apparatus and methods 2.2.1. Sorption apparatus The water vapor sorption apparatus consisted of a quartz spring placed in a water jacket glass cell with service lines to a solvent reservoir and to a pressure transducer. The details of the sorption apparatus are
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 1 6 7 - 4
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reported in a previous paper (Del Nobile, Mensitieri, Ho, Huang, & Nicolais, 1997). Water sorption tests were performed by increasing the external pressure in a stepwise manner. Diffusion coefficients evaluated from each sorption run were related to the average water concentration inside the polymer calculated as the mean of the initial and final equilibrium concentration. The step change of water activity in each run was about 0.1. 2.2.2. X-ray Wide angle X-ray diffraction patterns were obtained with nickel-filtered CuKa radiation using an automatic Philips powder diffractometer.
3. Results and discussions The permeability coefficient, P, is defined through the following expression: P¼
JSS l 1 p 0 ð aW
a2W Þ
;
ð1Þ
where JSS is the penetrant mass flux through polymer film at steady state, p0 is the water vapor pressure, l is the film thickness, a1W and a2W are the water activity at the upstream and downstream side of the film, respectively. According to Fick’s constitutive equation, JSS depends on the penetrant concentration gradient through the following relationship: ocW ; ð2Þ ox where cW is the concentration of water dissolved into the polymer, x is the spatial coordinate (unidimensional geometry) and DF ðcW Þ is the Fickian diffusivity. Usually, the diffusion coefficient depends only on the temperature (ideal Fickian diffusion); however, when the polymeric matrix is markedly swollen by the penetrant, and/or there are specific interactions between the polymer and the penetrant molecules, DF also depends on the local penetrant concentration. Integrating Eq. (2) from x ¼ 0 to x ¼ l and substituting JSS l with P ða1W a2W Þ (Eq. (1)) the following relationship is obtained: R c1W ða1W Þ DF ðcW Þ dcW 1 2 c2 ða2 Þ ; ð3Þ P aW ; aW ¼ W W 1 p0 ðaW a2W Þ JSS ¼ DF ðcW Þ
where c1W ða1W Þ and c2W ða2W Þ are the concentrations of the penetrant sorbed into the polymer at the upstream and downstream interfaces, respectively. Eq. (3) can be rearranged as follows: R c1W ða1W Þ DF ðcW Þ dcW c1 a1 c2 a2 1 2 c2W ða2W Þ W W W W P aW ; aW ¼ 1 1 ¼ DS; cW ðaW Þ c2W ða2W Þ p0 ða1W a2W Þ ð4Þ
where D and S are defined as the average diffusivity and solubility, respectively. As can be inferred from the above arguments, permeation of low molecular weight compounds through polymeric films is governed by both thermodynamics, S, and kinetics factors, D. To better illustrate these two distinct aspects of permeation of water through the investigated polyamides, the solubilization and diffusion process will be presented separately as follows. 3.1. Solubilization process Water sorption in moderately hydrophilic polymers, such as polyamides, is a rather complex phenomenon due to the presence of specific interactions between water molecules and the hydrophilic sites on the polymer backbone. In fact, the sorbed molecules are in part randomly dispersed into the polymer matrix (sorbed water) and in part physically bonded to the hydrophilic sites (adsorbed water) (Netti, Del Nobile, Mensitieri, Ambrosio, & Nicolais, 1996). Given the above scenario of the sorption process, the total amount of sorbed water can be expressed as follows: cW ¼ csW þ cad W;
ð5Þ
where cW is the total concentration of sorbed water, csW is the concentration of water randomly dispersed into the polymer matrix and cad W is the concentration of water physically bonded to the hydrophilic sites. As reported in a previous paper (Netti et al., 1996), the equation proposed by Flory (1953) to describe the mixing process of a linear polymer with a low molecular weight compound can be used to relate csW to water activity
Fig. 1. Equilibrium water concentration plotted as a function of water activity: ðÞ homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; (––) model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
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289
Table 1 Chemical structure of the investigated polyamides Sample
Substituting unit
Homopolymer
–
Repeating unit
n/m –
Copolymer A
0.023
Copolymer B
0.022
Copolymer C
0.019
csW qp =18 22:41 103 ðqW =qp Þ þ csW
lnðaW Þ ¼ ln þ
!
csW qp =18 1 22:41 103 ðqW =qp Þ þ csW
!
csW qp =18 þv 1 22:41 103 ðqW =qp Þ þ csW
!2 ð6Þ
;
where csW is expressed as cm3 ðSTPÞ=cm3 ðPolymerÞ; v is the Flory–Huggins interaction parameter, qp is the density of dry polymer expressed as g=cm3 ; qW is the density of the sorbed water expressed as g=cm3 ; aW is the water activity. The dependence of cad W on the water activity can be described by means of the Langmuir equation, which was successfully used to describe gas adsorption in zeolites: cad W ¼
CH0 baW ; 1 þ baW
ð7Þ
where b is the affinity constant between interactive sites and water molecules and CH0 is the adsorption capacity of the interactive sites. Fig. 1 shows the sorption isotherms at 25 °C of all the investigated samples. The curves shown in Fig. 1 represent the best fit of Eq. (5) to the experimental data.
Table 2 Parameters appearing in Eq. (5) obtained by fitting cW versus aW data Samples
v
CH0 ðcm3 ðSTPÞ=cm3 ðdry polymerÞÞ
b
Homopolymer Copolymer A Copolymer B Copolymer C
1.66 1.79 1.78 1.70
4.03 4.78 3.83 3.72
229 55.2 89.7 200
The values of the parameters appearing in Eq. (5) obtained by fitting the data are listed in Table 2. The good agreement between the model prediction (Eq. (5)) and the experimental data suggests that the sorption process of water in the investigated polyamides can be indeed described in terms of the dual sorption mechanism previously described. As shown in Fig. 1, the amount of water sorbed at equilibrium into the investigated copolymers is always lower than that sorbed in the homopolymer; even though there are only small differences among the behavior of the investigated films (see Table 1). In the case of semi-crystalline polymers, crystalline domains acting as impervious regions for diffusing molecules, reduce the amount of water sorbed into the polymer (Michaels & Bixler, 1961a,b; Michaels & Parker, 1959). Accordingly, the concentration of water sorbed into a semi-crystalline polymer at a given water activity is related to that of the totally amorphous polymer at the same water activity through the following relationship: cW ¼ ac W ;
ð8Þ
where a is the amorphous fraction of polymer, cW is the concentration of water sorbed into the semi-crystalline polymer at a given water activity, while c W is the
Table 3 Crystallinity level of the investigated samples Samples
Crystallinity level (%)
Homopolymer Copolymer A Copolymer B Copolymer C
0.40 0.38 0.33 0.41
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Table 4 Parameters appearing in Eq. (5) obtained by fitting c W versus aW data Samples
v
Homopolymer Copolymer A Copolymer B Copolymer C
1.29 1.46 1.49 1.31
[1.26–1.33] [1.42–1.50] [1.45–1.53] [1.28–1.36]
CH0 ðcm3 ðSTPÞ=cm3 ðdry polymerÞÞ
b
11.5 [8.14–16.6] 12.6 [8.99–17.7] 9.86 [6.75–14.5] 11.3 [8.18–16.5]
32.6 20.5 22.8 34.4
Mole of [13.6–165] [9.91–55.4] [10.5–78.2] [14.0–185]
=g dry polymers
8:85 103 8:82 103 8:74 103 8:73 103
The data reported in the squared brackets are the confidence interval relative to 95% probability.
concentration of water sorbed into the totally amorphous polymer at the same water activity. In order to assess the influence of crystalline domains on the water transport properties of the investigated polyamides, the crystallinity level of each sample was determined and the results are listed in Table 3. Fig. 2 shows c W plotted as a function of water activity for all the investigated samples. Because of the small difference between the crystallinity levels of the examined polyamides, the data reported in Figs. 1 and 2 show a similar behavior. The curves shown in Fig. 2 represent the best fit of Eq. (5) to the experimental data. The results obtained by fitting the data are listed in Table 4 along with the concentration of the amidic groups (express as moles of amidic group per gram of dry polymer). As reported in Table 4, the Flory interaction parameter v is approximately the same for the homopolymer and the copolymer C, and the for the copolymers A and B. The value of CH0 does not change among the investigated polyamides due to the constancy of the concentration of amidic groups. It is not possible to make any consideration on the parameter b due to the overlapping of its confidence intervals. From the above evidences it can be stated that the observed differences among the behaviors of the investigated polyamides have to be ascribed to the different affinity between the polymer and the water molecules (v). In particular, introducing the substituting
Fig. 2. c W plotted as a function of water activity: () homopolymer; (M) copolymer A; ( ) copolymer B; ðrÞ copolymer C; ð— —Þ model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
unit used to obtain the copolymer C does not modify the affinity with water with respect to the homopolymer. On the other hand the substituting unit used to obtain copolymers A and B reduce the affinity between water and polymer if compared to that of the homopolymer. 3.2. Diffusion process As previously reported the diffusion process can be described in terms of the Fickian constitutive equation (Eq. (2)). In order to determine the dependence of the Fickian diffusion coefficient on cW , water sorption tests, which were also used to evaluate the water sorption isotherms reported in Fig. 1, were performed by increasing the water vapor partial pressure in a stepwise manner. The difference between the initial and final water vapor partial pressure was sufficiently small to ensure the constancy of the diffusion coefficient during each sorption test. To evaluate the water diffusion coefficient, the sorption kinetic data were fitted by using the following expression: ( " #) 2 1 X MðtÞ 8 DF ð2n þ 1Þ p2 t ¼1 exp ; M1 4l2 ð2n þ 1Þ2 p2 n¼0 ð9Þ where MðtÞ is the amount of water sorbed at time t, M1 is the amount of water sorbed at equilibrium. Eq. (9) is the analytical solution of Fick’s second law for the specific case of diffusion through a plane sheet (Crank, 1975). Fig. 3 shows MðtÞ=M1 plotted as function of time (copolymer C) at four different activities along with the best fit of Eq. (9) to the experimental data. The fit of Eq. (9) to the data is quite satisfactory, confirming the constancy of the diffusion coefficient during each sorption test. As reported in a previous paper (Del Nobile et al., 1997), a simple expression to relate DF to local penetrant concentration can be obtained by rearranging the relationship proposed by Fujita (1961) to relate the thermodynamic diffusivity to the local penetrant concentration 1 DF ðcW Þ ¼ A1 exp ; ð10Þ A2 þ A3 c W
M.A. Del Nobile et al. / Journal of Food Engineering 53 (2002) 287–293
291
also reported the best fit of Eq. (10) of the experimental data, while the obtained model’s parameters are listed in Table 5. Contrarily to what was previously observed in the case of the sorption isotherms, there is a marked difference between the behavior of the homopolymer and that of the copolymers. The crystalline domains, present in semi-crystalline polymers, increasing the diffusive pathway of the water molecules reduce their diffusion coefficient (Michaels & Bixler, 1961a,b; Michaels & Parker, 1959). A simple way to relate the Fickian diffusion coefficient of a semicrystalline polymer to that of the totally amorphous polymer is that proposed by Paul (1979) Fig. 3. MðtÞ=M1 plotted as a function of time: ð Þ aW ¼ 0:05 ! aW ¼ 0:1; ( ) aW ¼ 0:4 ! aW ¼ 0:5; ðNÞ aW ¼ 0:6 ! aW ¼ 0:7; ðMÞ aW ¼ 0:8 ! aW ¼ 0:9.
where Ai ’s are constant. It is worth noting that the theoretical arguments used to derive Eq. (10) are no longer valid when this expression is used to describe the dependence of DF on cW ; hence, in the case under investigation Eq. (10) has to be regarded as an empirical equation. As a consequence, the parameters Ai ’s loose their original physical meaning and have to be regarded as fitting parameters. Fig. 4 shows the diffusion coefficient, evaluated according to the above method, plotted as a function of the average water concentration. In the same figure are
DF ¼ aD F ;
ð11Þ
where DF is the diffusivity of the semi-crystalline polymer, while D F is the diffusivity of the totally amorphous polymer. Fig. 5 shows D F plotted as a function of c Average (average water concentration dissolved into the amorphous fraction of the polymeric matrix). As one would expect, because of the small differences between the crystallinity levels of the examined polyamides, the data reported in Figs. 4 and 5 show a similar behavior. The curves reported in the same figure are the best fit of Eq. (10) to the experimental data. The above results suggest that introducing the substituting group used to obtain copolymer B results in an increase in the macromolecular mobility of the polymeric matrix with respect to the homopolymer. On the other hand, introducing the substituting group used to obtain copolymer C results in a decrease in the macromolecular mobility of the polymeric matrix with respect to the homopolymer. In the case of copolymer A, the introduction of the substituting group does not substantially change the macromolecular mobility of the polymeric matrix if compared to the homopolymer. 3.3. Permeation process
Fig. 4. Fickian diffusivity plotted as a function of average water concentration: ðÞ homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; ð— —Þ model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
In order to quantitatively determine the dependence of the permeability coefficient on the water activity at the upstream and downstream side of the film Eqs. (5) and (10) were used to evaluate the water concentration on both sides of the film and to describe the dependence DF on local water concentration
Table 5 Parameters appearing in Eq. (12) obtained by fitting DF versus cW data Samples
A1 ðcm2 =sÞ
A2
A3 ðcm3 ðSTPÞ= cm3 ðdry polymerÞÞ
Homopolymer Copolymer A Copolymer B Copolymer C
2:52 108 4:64 107 1:49 108 5:38 107
0.227 0.143 0.290 0.138
2:54 103 6:26 104 9:79 103 4:39 104
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Fig. 5. DT plotted as a function of average c W : homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; (— —) model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
P a1W ; a2W ¼
R c1W ða1W Þ c2W ða2W Þ
the homopolymer, while that of the other two copolymers is always lower than that of the homopolymer. The observed marked differences between the water permeabilities of the investigated polyamide films (Fig. 6) could be in principle ascribed to either differences in the chemical (repeating unit) or physical (degree of crystallinity) structure of the investigated polyamides or to both. However, because of the small difference among the crystallinity levels of the examined polyamides, the observed differences have to be ascribed to the differences in the chemical structure of the examined polyamides. In particular, the substituting chemical groups modify the macromolecular mobility of the polymeric matrix if compared to that of the homopolymer, while they do not change substantially the affinity between water molecules and the polymer.
4. Conclusion A1 exp ð 1=ðA2 þ A3 cW ÞÞ dcW p0 ða1W a2W Þ
: ð12Þ
Fig. 6 shows the permeability coefficient, as predicted by means of Eq. (12) using the data reported in Tables 2 and 5, plotted as a function of water activity at the upstream side of the film. In order to simulate a permeation test, the curves reported in the above figure were obtained by fixing the water activity at the downstream side of the film equal to zero. As one would expect the water permeability increases with the water activity at the upstream side of the film; besides, there is a substantial difference between the behaviors of the investigated polyamides. In particular, the water permeability of copolymer B is always higher than that of
Water sorption tests were experimentally determined for the four samples obtained by introducing different comonomers into the polymeric chain. The experimental data were fitted to obtain the diffusivity and solubility values needed to determine the permeability coefficients. It can be observed that only one sample presents better barrier properties respect to the homopolymer while the others show a worse behavior. The differences in water transport properties observed among the samples can be ascribed principally to the different chemical structures rather than to their physical characteristics. The crystallinity degree, in fact, is almost the same for all the samples while the substituting chemical groups really modify the macromolecular mobility of the polymeric matrix so that the behavior of the four samples is different.
Acknowledgements The authors wish to thank Armando Mariano (SNIA Ricerche, Via Pomarico s.n.c.-75010 Pisticci Scalo Italy) and Dr. Luciano Di Maio (University of Salerno) for supplying the polyamide samples. The work was funded under the ‘‘Progetto Finalizzato MSTA II’’ Program grants of the National Research Council.
References Fig. 6. Water permeability as predicted by Eq. (12) plotted as a function of water activity at the upstream side of the film: ð— —Þ homopolymer; (- - - -) copolymer A; (———) copolymer B; (— — ) copolymer C.
Crank, J. (1975). The mathematics of diffusion (2nd ed., pp. 47–49). Oxford: Clarendon Press. Del Nobile, M. A., Mensitieri, G., Ho, L. H., Huang, S. J., & Nicolais, L. (1997). Moisture transport properties of a degradable nylon
M.A. Del Nobile et al. / Journal of Food Engineering 53 (2002) 287–293 for food packaging. Packaging Technology and Science, 10, 311– 330. Flory, P. J. (1953). Principles of polymer chemistry (pp. 495–512). Ithaca: Cornell University Press. Fujita, H. (1961). Diffusion in polymer-diluent systems. Fortschritte der Hochpolymeren-Forschung, 3, 1–447. Michaels, A. S., & Bixler, H. J. (1961a). Solubility of gases in polyethylene. Journal of Polymer Science, 50, 393–412. Michaels, A. S., & Bixler, H. J. (1961b). Flow of gases through polyethylene. Journal of Polymer Science, 50, 413–439.
293
Michaels, A. S., & Parker, R. B., Jr. (1959). Sorption and flow of gases in polyethylene. Journal of Polymer Science, 41, 53– 71. Netti, P. A., Del Nobile, M. A., Mensitieri, G., Ambrosio, L., & Nicolais, L. (1996). Water transport in hyaluronic acid esters. Bioactive and Compatible Polymers, 11(4), 312–327. Paul, D. R. (1979). Gas sorption and transport in glassy polymer. Ber. Bunsengesellschaf Physical Chemistry, 83, 294–302. Rosen, S. L. (1982). Fundamental principles of polymeric materials (pp. 14–16). New York: Wiley.
Moisture transport properties of polyamides copolymers intended for food packaging applications M.A. Del Nobile b
a,*
, G.G. Buonocore
a,b
, L. Palmieri a, A. Aldi a, D. Acierno
a,b
a Instituto di Produzioni e Preparazioni Alimentari, University of Foggia, Via Napoli, 25 71100 Foggia, Italy Department of Materials and Production Engineering, University of Naples ‘Federico II’, P.le Tecchio 80, 80125 Naples, Italy
Received 16 March 2001; accepted 11 September 2001
Abstract In this paper the barrier properties of a series of polyamides used for food packaging applications were analyzed. In particular, permeation of water through the investigated polyamides was studied and water diffusivity and solubility were evaluated as a function of water concentration. Water vapor sorption tests were performed at 25 °C and at several water vapor activities on the four samples investigated. The obtained values were related to the macromolecular chain modification deriving from the introduction of different comonomers. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Water; Nylon; Sorption; Diffusion; Packaging
1. Introduction Polymeric materials are generally used in food packaging applications because they have, among other features, the capability to control the mass exchange of low molecular weight compounds between the foodstuff and its external environment. It is extremely important to guarantee the proper shelf life of the packed product. In fact, it must be considered that the degradation rate of the packed foodstuff can be decreased if the packaging material presents high barrier properties toward those specific compounds responsible for food degradation. Transport properties of oxygen, carbon dioxide, water, nitrogen and aromas through polymers are usually the more interesting to be assessed. The permeability of low molecular weight compounds through polymers usually spans a wide range of values permitting proper choice of the packaging materials for specific needs. Actually, the desired characteristics of a packaging material are obtained by laminating films with different properties. New materials based on polyamides can be developed, which present intrinsic barrier properties. In this way, the thickness of the film can be reduced and this can be considered an environmental advantage. *
Corresponding author. E-mail address: [email protected] (M.A. Del Nobile).
In the present paper water transport properties have been evaluated for polyamides, polymers generally used in packaging applications. In particular, the effect of copolymerization of Nylon 6,6 on its barrier properties has been studied. Different comonomers have been used and the different packaging materials obtained were characterized to understand how chemical and physical modifications of the polymer structure influence water permeability with respect to the homopolymer [an homopolymer is defined as a polymer consisting of chains that contain a single repeating unit (Rosen, 1982)].
2. Experimental 2.1. Materials The polyamide samples were supplied by SNIA Ricerche (Via Pomarico s.n.c. 75010 Pisticci Scalo Italy) as films, and were used as received. 2.2. Apparatus and methods 2.2.1. Sorption apparatus The water vapor sorption apparatus consisted of a quartz spring placed in a water jacket glass cell with service lines to a solvent reservoir and to a pressure transducer. The details of the sorption apparatus are
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 1 6 7 - 4
288
M.A. Del Nobile et al. / Journal of Food Engineering 53 (2002) 287–293
reported in a previous paper (Del Nobile, Mensitieri, Ho, Huang, & Nicolais, 1997). Water sorption tests were performed by increasing the external pressure in a stepwise manner. Diffusion coefficients evaluated from each sorption run were related to the average water concentration inside the polymer calculated as the mean of the initial and final equilibrium concentration. The step change of water activity in each run was about 0.1. 2.2.2. X-ray Wide angle X-ray diffraction patterns were obtained with nickel-filtered CuKa radiation using an automatic Philips powder diffractometer.
3. Results and discussions The permeability coefficient, P, is defined through the following expression: P¼
JSS l 1 p 0 ð aW
a2W Þ
;
ð1Þ
where JSS is the penetrant mass flux through polymer film at steady state, p0 is the water vapor pressure, l is the film thickness, a1W and a2W are the water activity at the upstream and downstream side of the film, respectively. According to Fick’s constitutive equation, JSS depends on the penetrant concentration gradient through the following relationship: ocW ; ð2Þ ox where cW is the concentration of water dissolved into the polymer, x is the spatial coordinate (unidimensional geometry) and DF ðcW Þ is the Fickian diffusivity. Usually, the diffusion coefficient depends only on the temperature (ideal Fickian diffusion); however, when the polymeric matrix is markedly swollen by the penetrant, and/or there are specific interactions between the polymer and the penetrant molecules, DF also depends on the local penetrant concentration. Integrating Eq. (2) from x ¼ 0 to x ¼ l and substituting JSS l with P ða1W a2W Þ (Eq. (1)) the following relationship is obtained: R c1W ða1W Þ DF ðcW Þ dcW 1 2 c2 ða2 Þ ; ð3Þ P aW ; aW ¼ W W 1 p0 ðaW a2W Þ JSS ¼ DF ðcW Þ
where c1W ða1W Þ and c2W ða2W Þ are the concentrations of the penetrant sorbed into the polymer at the upstream and downstream interfaces, respectively. Eq. (3) can be rearranged as follows: R c1W ða1W Þ DF ðcW Þ dcW c1 a1 c2 a2 1 2 c2W ða2W Þ W W W W P aW ; aW ¼ 1 1 ¼ DS; cW ðaW Þ c2W ða2W Þ p0 ða1W a2W Þ ð4Þ
where D and S are defined as the average diffusivity and solubility, respectively. As can be inferred from the above arguments, permeation of low molecular weight compounds through polymeric films is governed by both thermodynamics, S, and kinetics factors, D. To better illustrate these two distinct aspects of permeation of water through the investigated polyamides, the solubilization and diffusion process will be presented separately as follows. 3.1. Solubilization process Water sorption in moderately hydrophilic polymers, such as polyamides, is a rather complex phenomenon due to the presence of specific interactions between water molecules and the hydrophilic sites on the polymer backbone. In fact, the sorbed molecules are in part randomly dispersed into the polymer matrix (sorbed water) and in part physically bonded to the hydrophilic sites (adsorbed water) (Netti, Del Nobile, Mensitieri, Ambrosio, & Nicolais, 1996). Given the above scenario of the sorption process, the total amount of sorbed water can be expressed as follows: cW ¼ csW þ cad W;
ð5Þ
where cW is the total concentration of sorbed water, csW is the concentration of water randomly dispersed into the polymer matrix and cad W is the concentration of water physically bonded to the hydrophilic sites. As reported in a previous paper (Netti et al., 1996), the equation proposed by Flory (1953) to describe the mixing process of a linear polymer with a low molecular weight compound can be used to relate csW to water activity
Fig. 1. Equilibrium water concentration plotted as a function of water activity: ðÞ homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; (––) model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
M.A. Del Nobile et al. / Journal of Food Engineering 53 (2002) 287–293
289
Table 1 Chemical structure of the investigated polyamides Sample
Substituting unit
Homopolymer
–
Repeating unit
n/m –
Copolymer A
0.023
Copolymer B
0.022
Copolymer C
0.019
csW qp =18 22:41 103 ðqW =qp Þ þ csW
lnðaW Þ ¼ ln þ
!
csW qp =18 1 22:41 103 ðqW =qp Þ þ csW
!
csW qp =18 þv 1 22:41 103 ðqW =qp Þ þ csW
!2 ð6Þ
;
where csW is expressed as cm3 ðSTPÞ=cm3 ðPolymerÞ; v is the Flory–Huggins interaction parameter, qp is the density of dry polymer expressed as g=cm3 ; qW is the density of the sorbed water expressed as g=cm3 ; aW is the water activity. The dependence of cad W on the water activity can be described by means of the Langmuir equation, which was successfully used to describe gas adsorption in zeolites: cad W ¼
CH0 baW ; 1 þ baW
ð7Þ
where b is the affinity constant between interactive sites and water molecules and CH0 is the adsorption capacity of the interactive sites. Fig. 1 shows the sorption isotherms at 25 °C of all the investigated samples. The curves shown in Fig. 1 represent the best fit of Eq. (5) to the experimental data.
Table 2 Parameters appearing in Eq. (5) obtained by fitting cW versus aW data Samples
v
CH0 ðcm3 ðSTPÞ=cm3 ðdry polymerÞÞ
b
Homopolymer Copolymer A Copolymer B Copolymer C
1.66 1.79 1.78 1.70
4.03 4.78 3.83 3.72
229 55.2 89.7 200
The values of the parameters appearing in Eq. (5) obtained by fitting the data are listed in Table 2. The good agreement between the model prediction (Eq. (5)) and the experimental data suggests that the sorption process of water in the investigated polyamides can be indeed described in terms of the dual sorption mechanism previously described. As shown in Fig. 1, the amount of water sorbed at equilibrium into the investigated copolymers is always lower than that sorbed in the homopolymer; even though there are only small differences among the behavior of the investigated films (see Table 1). In the case of semi-crystalline polymers, crystalline domains acting as impervious regions for diffusing molecules, reduce the amount of water sorbed into the polymer (Michaels & Bixler, 1961a,b; Michaels & Parker, 1959). Accordingly, the concentration of water sorbed into a semi-crystalline polymer at a given water activity is related to that of the totally amorphous polymer at the same water activity through the following relationship: cW ¼ ac W ;
ð8Þ
where a is the amorphous fraction of polymer, cW is the concentration of water sorbed into the semi-crystalline polymer at a given water activity, while c W is the
Table 3 Crystallinity level of the investigated samples Samples
Crystallinity level (%)
Homopolymer Copolymer A Copolymer B Copolymer C
0.40 0.38 0.33 0.41
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Table 4 Parameters appearing in Eq. (5) obtained by fitting c W versus aW data Samples
v
Homopolymer Copolymer A Copolymer B Copolymer C
1.29 1.46 1.49 1.31
[1.26–1.33] [1.42–1.50] [1.45–1.53] [1.28–1.36]
CH0 ðcm3 ðSTPÞ=cm3 ðdry polymerÞÞ
b
11.5 [8.14–16.6] 12.6 [8.99–17.7] 9.86 [6.75–14.5] 11.3 [8.18–16.5]
32.6 20.5 22.8 34.4
Mole of [13.6–165] [9.91–55.4] [10.5–78.2] [14.0–185]
=g dry polymers
8:85 103 8:82 103 8:74 103 8:73 103
The data reported in the squared brackets are the confidence interval relative to 95% probability.
concentration of water sorbed into the totally amorphous polymer at the same water activity. In order to assess the influence of crystalline domains on the water transport properties of the investigated polyamides, the crystallinity level of each sample was determined and the results are listed in Table 3. Fig. 2 shows c W plotted as a function of water activity for all the investigated samples. Because of the small difference between the crystallinity levels of the examined polyamides, the data reported in Figs. 1 and 2 show a similar behavior. The curves shown in Fig. 2 represent the best fit of Eq. (5) to the experimental data. The results obtained by fitting the data are listed in Table 4 along with the concentration of the amidic groups (express as moles of amidic group per gram of dry polymer). As reported in Table 4, the Flory interaction parameter v is approximately the same for the homopolymer and the copolymer C, and the for the copolymers A and B. The value of CH0 does not change among the investigated polyamides due to the constancy of the concentration of amidic groups. It is not possible to make any consideration on the parameter b due to the overlapping of its confidence intervals. From the above evidences it can be stated that the observed differences among the behaviors of the investigated polyamides have to be ascribed to the different affinity between the polymer and the water molecules (v). In particular, introducing the substituting
Fig. 2. c W plotted as a function of water activity: () homopolymer; (M) copolymer A; ( ) copolymer B; ðrÞ copolymer C; ð— —Þ model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
unit used to obtain the copolymer C does not modify the affinity with water with respect to the homopolymer. On the other hand the substituting unit used to obtain copolymers A and B reduce the affinity between water and polymer if compared to that of the homopolymer. 3.2. Diffusion process As previously reported the diffusion process can be described in terms of the Fickian constitutive equation (Eq. (2)). In order to determine the dependence of the Fickian diffusion coefficient on cW , water sorption tests, which were also used to evaluate the water sorption isotherms reported in Fig. 1, were performed by increasing the water vapor partial pressure in a stepwise manner. The difference between the initial and final water vapor partial pressure was sufficiently small to ensure the constancy of the diffusion coefficient during each sorption test. To evaluate the water diffusion coefficient, the sorption kinetic data were fitted by using the following expression: ( " #) 2 1 X MðtÞ 8 DF ð2n þ 1Þ p2 t ¼1 exp ; M1 4l2 ð2n þ 1Þ2 p2 n¼0 ð9Þ where MðtÞ is the amount of water sorbed at time t, M1 is the amount of water sorbed at equilibrium. Eq. (9) is the analytical solution of Fick’s second law for the specific case of diffusion through a plane sheet (Crank, 1975). Fig. 3 shows MðtÞ=M1 plotted as function of time (copolymer C) at four different activities along with the best fit of Eq. (9) to the experimental data. The fit of Eq. (9) to the data is quite satisfactory, confirming the constancy of the diffusion coefficient during each sorption test. As reported in a previous paper (Del Nobile et al., 1997), a simple expression to relate DF to local penetrant concentration can be obtained by rearranging the relationship proposed by Fujita (1961) to relate the thermodynamic diffusivity to the local penetrant concentration 1 DF ðcW Þ ¼ A1 exp ; ð10Þ A2 þ A3 c W
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also reported the best fit of Eq. (10) of the experimental data, while the obtained model’s parameters are listed in Table 5. Contrarily to what was previously observed in the case of the sorption isotherms, there is a marked difference between the behavior of the homopolymer and that of the copolymers. The crystalline domains, present in semi-crystalline polymers, increasing the diffusive pathway of the water molecules reduce their diffusion coefficient (Michaels & Bixler, 1961a,b; Michaels & Parker, 1959). A simple way to relate the Fickian diffusion coefficient of a semicrystalline polymer to that of the totally amorphous polymer is that proposed by Paul (1979) Fig. 3. MðtÞ=M1 plotted as a function of time: ð Þ aW ¼ 0:05 ! aW ¼ 0:1; ( ) aW ¼ 0:4 ! aW ¼ 0:5; ðNÞ aW ¼ 0:6 ! aW ¼ 0:7; ðMÞ aW ¼ 0:8 ! aW ¼ 0:9.
where Ai ’s are constant. It is worth noting that the theoretical arguments used to derive Eq. (10) are no longer valid when this expression is used to describe the dependence of DF on cW ; hence, in the case under investigation Eq. (10) has to be regarded as an empirical equation. As a consequence, the parameters Ai ’s loose their original physical meaning and have to be regarded as fitting parameters. Fig. 4 shows the diffusion coefficient, evaluated according to the above method, plotted as a function of the average water concentration. In the same figure are
DF ¼ aD F ;
ð11Þ
where DF is the diffusivity of the semi-crystalline polymer, while D F is the diffusivity of the totally amorphous polymer. Fig. 5 shows D F plotted as a function of c Average (average water concentration dissolved into the amorphous fraction of the polymeric matrix). As one would expect, because of the small differences between the crystallinity levels of the examined polyamides, the data reported in Figs. 4 and 5 show a similar behavior. The curves reported in the same figure are the best fit of Eq. (10) to the experimental data. The above results suggest that introducing the substituting group used to obtain copolymer B results in an increase in the macromolecular mobility of the polymeric matrix with respect to the homopolymer. On the other hand, introducing the substituting group used to obtain copolymer C results in a decrease in the macromolecular mobility of the polymeric matrix with respect to the homopolymer. In the case of copolymer A, the introduction of the substituting group does not substantially change the macromolecular mobility of the polymeric matrix if compared to the homopolymer. 3.3. Permeation process
Fig. 4. Fickian diffusivity plotted as a function of average water concentration: ðÞ homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; ð— —Þ model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
In order to quantitatively determine the dependence of the permeability coefficient on the water activity at the upstream and downstream side of the film Eqs. (5) and (10) were used to evaluate the water concentration on both sides of the film and to describe the dependence DF on local water concentration
Table 5 Parameters appearing in Eq. (12) obtained by fitting DF versus cW data Samples
A1 ðcm2 =sÞ
A2
A3 ðcm3 ðSTPÞ= cm3 ðdry polymerÞÞ
Homopolymer Copolymer A Copolymer B Copolymer C
2:52 108 4:64 107 1:49 108 5:38 107
0.227 0.143 0.290 0.138
2:54 103 6:26 104 9:79 103 4:39 104
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Fig. 5. DT plotted as a function of average c W : homopolymer; ðMÞ copolymer A; ( ) copolymer B; ðrÞ copolymer C; (— —) model best fit of homopolymer data; (- - - -) model best fit of copolymer A data; (———) model best fit of copolymer B data; (— — ) model best fit of copolymer C data.
P a1W ; a2W ¼
R c1W ða1W Þ c2W ða2W Þ
the homopolymer, while that of the other two copolymers is always lower than that of the homopolymer. The observed marked differences between the water permeabilities of the investigated polyamide films (Fig. 6) could be in principle ascribed to either differences in the chemical (repeating unit) or physical (degree of crystallinity) structure of the investigated polyamides or to both. However, because of the small difference among the crystallinity levels of the examined polyamides, the observed differences have to be ascribed to the differences in the chemical structure of the examined polyamides. In particular, the substituting chemical groups modify the macromolecular mobility of the polymeric matrix if compared to that of the homopolymer, while they do not change substantially the affinity between water molecules and the polymer.
4. Conclusion A1 exp ð 1=ðA2 þ A3 cW ÞÞ dcW p0 ða1W a2W Þ
: ð12Þ
Fig. 6 shows the permeability coefficient, as predicted by means of Eq. (12) using the data reported in Tables 2 and 5, plotted as a function of water activity at the upstream side of the film. In order to simulate a permeation test, the curves reported in the above figure were obtained by fixing the water activity at the downstream side of the film equal to zero. As one would expect the water permeability increases with the water activity at the upstream side of the film; besides, there is a substantial difference between the behaviors of the investigated polyamides. In particular, the water permeability of copolymer B is always higher than that of
Water sorption tests were experimentally determined for the four samples obtained by introducing different comonomers into the polymeric chain. The experimental data were fitted to obtain the diffusivity and solubility values needed to determine the permeability coefficients. It can be observed that only one sample presents better barrier properties respect to the homopolymer while the others show a worse behavior. The differences in water transport properties observed among the samples can be ascribed principally to the different chemical structures rather than to their physical characteristics. The crystallinity degree, in fact, is almost the same for all the samples while the substituting chemical groups really modify the macromolecular mobility of the polymeric matrix so that the behavior of the four samples is different.
Acknowledgements The authors wish to thank Armando Mariano (SNIA Ricerche, Via Pomarico s.n.c.-75010 Pisticci Scalo Italy) and Dr. Luciano Di Maio (University of Salerno) for supplying the polyamide samples. The work was funded under the ‘‘Progetto Finalizzato MSTA II’’ Program grants of the National Research Council.
References Fig. 6. Water permeability as predicted by Eq. (12) plotted as a function of water activity at the upstream side of the film: ð— —Þ homopolymer; (- - - -) copolymer A; (———) copolymer B; (— — ) copolymer C.
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